OMM 2004 Problem 1

Find all the prime number $p, q$ and r with $p < q < r$ , such that $25pq + r = 2004$ and $pqr + 1$ is a perfect square.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.